In studies for a medication, 10 percent of patients gained weight as a side effe

Question

In studies for a medication,

10

percent of patients gained weight as a side effect. Suppose

525

patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

(a) exactly

61

patients will gain weight as a side effect.

(b)

61

or fewer patients will gain weight as a side effect.

(c)

65

or more patients will gain weight as a side effect.

(d) between

61

and

65

,

inclusive, will gain weight as a side effect.

(a)

P(Xequals

61)equalsnothing

(Round to four decimal places as needed)

(b)

P(Xless than or equals

61)equalsnothing

(Round to four decimal places as needed)

(c)

P(Xgreater than or equals

65)equalsnothing

(Round to four decimal places as needed)

(d)

P(61

less than or equalsXless than or equals65)equalsnothing(Round to four decimal places as needed)

Explanation / Answer

mean = 525 * 0.1 = 52.5

standard deviation = sqrt(525 * 0.1 * 0.9) = 6.874

a)

P(X=61) = 525C61 * 0.1^61 * 0.9 ^ 464

= 0.026

b)

P(X < 61)

= P(Z < 61 - 52.5/6.874)

= P(Z < 1.237)

= 0.892

c)

P(X > 65) = P(Z > 65 - 52.5/6.874)

= P(Z > 1.819)

= 0.0345

d)

P(61 <= X <=65)

= P(X < 65) - P(X < 61)

= 1- 0.0345 - 0.892

= 0.0735

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.